Abstract
Background
When implementing new statistical procedures, there is often a need for simple—and yet computationally efficient—ways of numerically evaluating composite distribution functions. If the statistical procedure must support calculations for censored and noncensored cases, those calculations should be carried out using efficient computational implementations of both definite and indefinite integrals (e.g., calculation of tail areas of distribution functions).
Method
We developed a generic function evaluator such that users may specify a function using reverse Polish notation. As its argument the function evaluator takes a matrix of pointers and then applies the rows of this matrix to its internally defined stack of pointers. Accordingly, each row of the argument matrix defines a single operation such as evaluating a function on the current element of the stack, applying an algebraic operation to the two top elements of the stack, or manipulating the stack itself. Defining new composite distribution functions from other (atomic) distribution functions then corresponds to joining two or more function-defining matrices vertically. This approach can further be used to obtain integrals of any defined function. As an example we show how the density and distribution function for the minimum of two Weibull distributed random variables can be numerically evaluated and integrated.
Results
The procedure provides a flexible and extensible framework for implementing numerical evaluation of general, composite distributions. The procedure is numerically relatively efficient, although not optimal.